New footage aired on Iranian state television shows a US Navy sailor, who was among the 10 briefly held in Iranian custody, apologising for the international incident. US authorities said the video appears to be authentic but it was unclear under what circumstances the apology was made.

"It was a mistake that was our fault, and we apologise for our mistake," the sailor said. The sailor is asked whether the GPS showed the ships had crossed into Iranian territorial waters. He reportedly replied, "I believe so."

According to NBC News, US Central Command said that video "appears to be authentic but we cannot speak to the conditions of the situation or what the crew was experiencing at the time." A US military official added: "Clearly this staged video exhibits a sailor making an apology in an unknown context as an effort to defuse a tense situation and protect his crew."

The sailors were on their way to Bahrain when they were taken into custody on 12 January after their two small US Navy riverine vessels crossed into Iranian territory. The 10 sailors, nine men and one woman, were held overnight on Farsi Island and released on Wednesday (13 January).

The US Navy confirmed that the sailors were "safely returned" after leaving Iran's Farsi Island at 3.43am EST/8.43am GMT aboard the vessels they had been operating. In a statement, Iran's Revolutionary Guards said the sailors had been released back to international waters following a US apology and confirmation that it was "a mistake." US officials, however, said the government did not issue an apology.

"I can say unequivocally, the US government did not apologise to the government of Iran in any way during the course of this," a senior State Department official told NBC News. "We did provide context, we did explain that this was basically a routine transmission that had not intended to end up anywhere on Farsi Island or in Iranian territorial waters." The official said that Secretary of State John Kerry had spoken at least five times with Iranian Foreign Minister Javad Zarif during the incident.

In an address on 13 January, Kerry said, "All indications (were) that our sailors were well taken care of." According to Fox News, the Secretary of State cited the peaceful resolution as a "testament" to diplomacy and a new US-Iran relationship.